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nd 1; denotes the average wave strength component; is a limiter. The MUSCL type limiter of Van Leer is used, which has moderate dissipative and compressible performance; is a dissipative function put forward by Harten. The definitions of all these variables are given in Ref.[10]. The ratio between time and space is (14) where denotes the distance of the barycenters between element and satellite element 1. Eqs. (12) and (13) concern four satellite elements around the element , but the limiter function concerns another four satellite elements, so this scheme concerns eight satellite elements in all. 5. BOUNDARY CONDITIONS The boundaries of the computational domain have land boundaries (solid boundaries) and water boundaries (open boundaries) for a general shallow water problem. In the case of solid boundaries, no-slip or slip boundary conditions is considered on the basis of whether considering turbulent viscosity or not. Generally speaking, no-slip boundary conditions are given if considering turbulent viscosity, otherwise slip conditions are specified. The open boundary conditions, however, need to have a particular treatment. The local value of Froude number or whether the flow is subcritical or supercritical is the basis of determining the number of boundary conditions. For supercritical flow, three conditions at the inflow boundary and none at the outflow boundary must specified. For subcritical flow, two external conditions are specified at inflow boundary and one is required at the outflow boundary. 6. APPLICATIONS OF DAM-BREAK COMPUTATION Through the computation of 1D dam-break waves in a horizontal and frictionless channel and the comparison with Stoker's theoretical solution, it is shown that steep and nonoscillatory numerical solutions could be obtained using the hybrid type of TVD scheme . Two typical examples of 2D dam-break problems are solved and discussed by solving the shallow water equations using above finite volume TVD scheme. 6.1 Rectangular Dam-Break Consider a 2D partial dam-break model with a non-symmetrical breach. It is assumed that in the center of a 200m×200m channel, a partial dam breaking takes place instantaneously. The breach is 75m in length, which has distances of 30m from the left bank and 95m from the right. The initial water height is 10m and 5m respectively. No slope and friction are considered. The results displaying the views of the water surface elevation, contour of the surface elevation and velocity field are shown in Figure3 at time t=7.2s after the dam failure. At the instant of breaking of the dam, water is released through the breach, forming a positive wave propagating downstream and a negative wave spreading upstream. These results agree quite well with the results of using finite difference hybrid type of TVD scheme and those in Ref. . Fig. 3(a) Water surface elevation for a rectangular dam-break Fig. 3(b) Contour of surface elevation for a rectangular dam-break 6.2 Circular Dam-Break Another typical example is based on the hypothetical test case studied by Alcrudo and Garcia-Navarro [7], which involves the breaking of a circular dam. It is an important test example for the analysis of the algorithm performance and solving a complex shallow water problem. The physical model is that two regions of still water are separated by a cylindrical wall of radius 11m.